The binary ionic compound of magnesium and chlorine is magnesium chloride, with the chemical formula MgCl₂.

Here's why:

* Magnesium (Mg) is a metal in Group 2 of the periodic table, meaning it forms a +2 cation (Mg²⁺).

* Chlorine (Cl) is a nonmetal in Group 17, meaning it forms a -1 anion (Cl⁻).

To create a neutral compound, two chloride ions (2 x -1 = -2) are needed to balance the +2 charge of the magnesium ion. This results in the formula MgCl₂.